Priors for joint distribution set on marginal probabilities

[jsocolar]

I don’t have any brilliant suggestions, but you might find this helpful (as well as a few replies up-thread from there). (The title of the thread seems off-topic, but this is way downthread).

Do I need Jacobian adjustment here?

One way to reframe this is is to emphasize that Bayesian inference requires a prior distribution over the entire model configuration space. That can be constructed from independent priors on each of the nominal parameters, but such a prior is often not consistent with the entirety of our domain expertise. We not only need to carefully investigate the consequences of the prior model but also recognize that concepts like “informative” are context dependent and a prior that seems “noninformative…